1. **State the problem:** Simplify the expression $2\sqrt{616}$. 2. **Recall the formula and rules:** The square root of a product can be expressed as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ We want to simplify $\sqrt{616}$ by factoring out perfect squares. 3. **Factor 616:** $$616 = 4 \times 154$$ Since 4 is a perfect square, we can write: $$\sqrt{616} = \sqrt{4 \times 154} = \sqrt{4} \times \sqrt{154} = 2\sqrt{154}$$ 4. **Substitute back into the original expression:** $$2\sqrt{616} = 2 \times 2\sqrt{154} = 4\sqrt{154}$$ 5. **Check if $\sqrt{154}$ can be simplified further:** Factor 154: $$154 = 2 \times 7 \times 11$$ No perfect square factors other than 1, so $\sqrt{154}$ is simplified. **Final answer:** $$2\sqrt{616} = 4\sqrt{154}$$